How To Smooth Shade Newly Added Mesh To an Already Smooth Shaded Object
Okay so I found the answer after playing around with it for a little bit. 

What you need to do is select the new rough mesh you want to smooth in edit 
mode and press P to separate "Selection" as suggested by @Jagredom .

Then with the mesh selected click on the smooth shading button from Object mode. 

After this you have to switch to edit mode with the mesh still selected and click on the recalculate normals button under the Shading/UV Tab. This will get the mesh smooth and uniform with the full object.

Then you can rejoin the two objects by clicking on both of them while holding shift and then pressing ctrl + J